Last week, the City Council of Berkeley, California, unanimously voted for a new ordinance that would require cell phone retailers to advise customers to keep their handset out of pockets or bras when the device is connected to a wireless network. The rationale for the warning, which is based upon federal guidelines for limiting exposure to radio waves from wireless devices, doesn't look well-founded.
Unlike exposure to the X-rays used in a doctor's office or the gamma rays produced by radioactive elements like uranium or plutonium, which result in negative health consequences as exposure increases, radio transmitters in cell phones do not produce ionizing radiation. Although scientists have recently warned of the long-term risks of cell phone use related to the electromagnetic waves the devices emit, the evidence still is not strong enough to establish causality, only concern.
While some researchers urge cautious use of wireless devices, the National Institute of Health, Food and Drug Administration, American Cancer Society and Centers for Disease Control have found no evidence of cancer risks from cell phone use to date. Using a cell phone exposes you to no ionizing radiation at all. As far as we know, cell phones do not give you brain cancer. (If you're still worried, though, there's no harm in keeping your cell phone in a purse instead of your bra or on your belt instead of a pants pocket.)
For more context on the danger from different amounts of ionizing radiation, take a look at the following radiation webcomic by Randall Munroe of xkcd. As you can see, being directly exposed to a nuclear power plant meltdown is fatal; flying across North America or getting an X-ray at the dentist's office, not so much. You'll notice that cell phones do not appear in the graphic.